Dedicated, if you are looking for absolute Internet anonymity from websites you visit, then Pel is correct, you need a proxy (such as Tor). If you are just looking for protection from content filtering or spying by your ISP, then a VPN is what you are looking for.
This is the VPN I was using:
http://hidemyass.com/vpn/
I typically got close to 10Mbps from the HMA VPN, so it's a pretty good one. And with a VPN like HMA,
yes you will be anonymous to your ISP. Your ISP can't see anything you are doing when you are connected to the VPN. The only thing they will be able to see is that encrypted IPsec traffic is coming out of the WAN interface on your cable modem and destined for an IP address off their network. They have no way of seeing what websites you go to or any of the content within that encrypted traffic stream.
To break it down simply, you initiate a VPN connection from your computer to an IP address on an HMA VPN concentrator. Once that connection is established, it creates a tunnel through the Internet to this VPN concentrator. This VPN concentrator acts as a router for you and NATs all traffic back to you across the VPN connection. So this means anyone you communicate with will only see the IP address of the HMA VPN concentrator. This effectively makes you anonymous.
If you want ultra security (and based on what you said, you won't need this), you can also configure your PC to connect to a proxy, preferably Tor, in addition to the VPN. So you would have a VPN connection protecting you from snooping by your ISP, then you would bounce your communications through the Tor proxy network. I don't think all the Chinese spies in the world could track you with a setup like that. Of course, there are also a lot of other things you'd need to do at the application level to make sure you aren't leaking information out from your browser or cookies or whatnot.
But, if you just want to be able to bittorrent or prevent your ISP from snooping, then HMA VPN is the way to go.